For how many ordered pairs (A,B) where A and B are positive integers is $AAA_7+BBB_7+111_7=666_7?$
+2666 Because they are on the same bases, we can disregard them.
Now, we have the equation: \(AAA + BBB + 111 = 666\)
This means \(A + B = 5\)
The only possible cases are \((1,4)\), \((2,3)\), \((3,2)\), and \((4,1)\). Thus, are only \(\color{brown}\boxed{4}\) cases that
